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The Resource Cohomological induction and unitary representations, Anthony W. Knapp and David A. Vogan, Jr

Cohomological induction and unitary representations, Anthony W. Knapp and David A. Vogan, Jr

Work
Publication
Extent
1 online resource (xvii, 948 pages)
Contents
  • 5. Abstract Construction6. Hecke Algebras for Pairs (g, K); II. THE CATEGORY C(g, K); 1. Functors P and I; 2. Properties of P and I; 3. Constructions within C(g, K); 4. Special Properties of P and I in Examples; 5. Mackey Isomorphisms; 6. Derived Functors of P and I; 7. Standard Resolutions; 8. Koszul Resolution as a Complex; 9. Reduction of Exactness for the Koszul Resolution; 10. Exactness in the Abelian Case; III. DUALITY THEOREM; 1. Easy Duality; 2. Statement of Hard Duality; 3. Complexes for Computing Pj and Iĵ; 4. Hard Duality as a K Isomorphism; 5. Proof of g Equivariance in Case (i)
  • 6. Motivation for g Equivariance in Case (ii)7. Proof of g Equivariance in Case (ii); 8. Proof of Hard Duality in the General Case; IV. REDUCTIVE PAIRS; 1. Review of Cartan-Weyl Theory; 2. Cartan-Weyl Theory for Disconnected Groups; 3. Reductive Groups and Reductive Pairs; 4. Cartan Subpairs; 5. Finite-Dimensional Representations; 6. Parabolic Subpairs; 7. Harish-Chandra Isomorphism; 8. Infinitesimal Character; 9. Kostant's Theorem; 10. Casselman-Osborne Theorem; 11. Algebraic Analog of Bott-Borel-Weil Theorem; V. COHOMOLOGICAL INDUCTION; 1. Setting; 2. Effect on Infinitesimal Character
  • 3. Preliminary Lemmas4. Upper Bound on Multiplicities of K Types; 5. An Euler-Poincaré Principle for K Types; 6. Bottom-Layer Map; 7. Vanishing Theorem; 8. Fundamental Spectral Sequences; 9. Spectral Sequences for Analysis of K Types; 10. Hochschild-Serre Spectral Sequences; 11. Composite P Functors and I Functors; VI. SIGNATURE THEOREM; 1. Setting; 2. Hermitian Dual and Signature; 3. Hermitian Duality Relative to P and I; 4. Statement of Signature Theorem; 5. Comparison of Shapovalov Forms on K and G; 6. Preservation of Positivity from L)"K to K
  • 7. Signature Theorem for K Badly DisconnectedVII. TRANSLATION FUNCTORS; 1. Motivation and Examples; 2. Generalized Infinitesimal Character; 3. Chevalley's Structure Theorem for Z(g); 4. Z(l) Finiteness of u Homology and Cohomology; 5. Invariants in the Symmetric Algebra; 6 . Kostant's Theory of Harmonics; 7. Dixmier-Duflo Theorem; 8 . Translation Functors; 9. Integral Dominance; 10. Overview of Preservation of Irreducibility; 11. Details of Irreducibility; 12. Nonvanishing of Certain Translation Functors; 13. Application to (g, K) Modules with K Connected
Isbn
9781400883936
Instance
Label
Cohomological induction and unitary representations
Title
Cohomological induction and unitary representations
Statement of responsibility
Anthony W. Knapp and David A. Vogan, Jr
Creator
Contributor
Author
Subject
Genre
Language
eng
Member of
Cataloging source
N$T
http://library.link/vocab/creatorName
Knapp, Anthony W
Index
index present
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1954-
http://library.link/vocab/relatedWorkOrContributorName
Vogan, David A.
Series statement
Princeton mathematical series
Series volume
45
http://library.link/vocab/subjectName
  • Semisimple Lie groups
  • Representations of groups
  • Homology theory
  • Harmonic analysis
  • MATHEMATICS
  • MATHEMATICS
  • Harmonic analysis
  • Homology theory
  • Representations of groups
  • Semisimple Lie groups
Label
Cohomological induction and unitary representations, Anthony W. Knapp and David A. Vogan, Jr
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 5. Abstract Construction6. Hecke Algebras for Pairs (g, K); II. THE CATEGORY C(g, K); 1. Functors P and I; 2. Properties of P and I; 3. Constructions within C(g, K); 4. Special Properties of P and I in Examples; 5. Mackey Isomorphisms; 6. Derived Functors of P and I; 7. Standard Resolutions; 8. Koszul Resolution as a Complex; 9. Reduction of Exactness for the Koszul Resolution; 10. Exactness in the Abelian Case; III. DUALITY THEOREM; 1. Easy Duality; 2. Statement of Hard Duality; 3. Complexes for Computing Pj and Iĵ; 4. Hard Duality as a K Isomorphism; 5. Proof of g Equivariance in Case (i)
  • 6. Motivation for g Equivariance in Case (ii)7. Proof of g Equivariance in Case (ii); 8. Proof of Hard Duality in the General Case; IV. REDUCTIVE PAIRS; 1. Review of Cartan-Weyl Theory; 2. Cartan-Weyl Theory for Disconnected Groups; 3. Reductive Groups and Reductive Pairs; 4. Cartan Subpairs; 5. Finite-Dimensional Representations; 6. Parabolic Subpairs; 7. Harish-Chandra Isomorphism; 8. Infinitesimal Character; 9. Kostant's Theorem; 10. Casselman-Osborne Theorem; 11. Algebraic Analog of Bott-Borel-Weil Theorem; V. COHOMOLOGICAL INDUCTION; 1. Setting; 2. Effect on Infinitesimal Character
  • 3. Preliminary Lemmas4. Upper Bound on Multiplicities of K Types; 5. An Euler-Poincaré Principle for K Types; 6. Bottom-Layer Map; 7. Vanishing Theorem; 8. Fundamental Spectral Sequences; 9. Spectral Sequences for Analysis of K Types; 10. Hochschild-Serre Spectral Sequences; 11. Composite P Functors and I Functors; VI. SIGNATURE THEOREM; 1. Setting; 2. Hermitian Dual and Signature; 3. Hermitian Duality Relative to P and I; 4. Statement of Signature Theorem; 5. Comparison of Shapovalov Forms on K and G; 6. Preservation of Positivity from L)"K to K
  • 7. Signature Theorem for K Badly DisconnectedVII. TRANSLATION FUNCTORS; 1. Motivation and Examples; 2. Generalized Infinitesimal Character; 3. Chevalley's Structure Theorem for Z(g); 4. Z(l) Finiteness of u Homology and Cohomology; 5. Invariants in the Symmetric Algebra; 6 . Kostant's Theory of Harmonics; 7. Dixmier-Duflo Theorem; 8 . Translation Functors; 9. Integral Dominance; 10. Overview of Preservation of Irreducibility; 11. Details of Irreducibility; 12. Nonvanishing of Certain Translation Functors; 13. Application to (g, K) Modules with K Connected
Control code
ocn948756447
Dimensions
unknown
Extent
1 online resource (xvii, 948 pages)
File format
unknown
Form of item
online
Isbn
9781400883936
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
JSTOR
http://library.link/vocab/ext/overdrive/overdriveId
22573/ctt1bqrqp3
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)948756447
Label
Cohomological induction and unitary representations, Anthony W. Knapp and David A. Vogan, Jr
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 5. Abstract Construction6. Hecke Algebras for Pairs (g, K); II. THE CATEGORY C(g, K); 1. Functors P and I; 2. Properties of P and I; 3. Constructions within C(g, K); 4. Special Properties of P and I in Examples; 5. Mackey Isomorphisms; 6. Derived Functors of P and I; 7. Standard Resolutions; 8. Koszul Resolution as a Complex; 9. Reduction of Exactness for the Koszul Resolution; 10. Exactness in the Abelian Case; III. DUALITY THEOREM; 1. Easy Duality; 2. Statement of Hard Duality; 3. Complexes for Computing Pj and Iĵ; 4. Hard Duality as a K Isomorphism; 5. Proof of g Equivariance in Case (i)
  • 6. Motivation for g Equivariance in Case (ii)7. Proof of g Equivariance in Case (ii); 8. Proof of Hard Duality in the General Case; IV. REDUCTIVE PAIRS; 1. Review of Cartan-Weyl Theory; 2. Cartan-Weyl Theory for Disconnected Groups; 3. Reductive Groups and Reductive Pairs; 4. Cartan Subpairs; 5. Finite-Dimensional Representations; 6. Parabolic Subpairs; 7. Harish-Chandra Isomorphism; 8. Infinitesimal Character; 9. Kostant's Theorem; 10. Casselman-Osborne Theorem; 11. Algebraic Analog of Bott-Borel-Weil Theorem; V. COHOMOLOGICAL INDUCTION; 1. Setting; 2. Effect on Infinitesimal Character
  • 3. Preliminary Lemmas4. Upper Bound on Multiplicities of K Types; 5. An Euler-Poincaré Principle for K Types; 6. Bottom-Layer Map; 7. Vanishing Theorem; 8. Fundamental Spectral Sequences; 9. Spectral Sequences for Analysis of K Types; 10. Hochschild-Serre Spectral Sequences; 11. Composite P Functors and I Functors; VI. SIGNATURE THEOREM; 1. Setting; 2. Hermitian Dual and Signature; 3. Hermitian Duality Relative to P and I; 4. Statement of Signature Theorem; 5. Comparison of Shapovalov Forms on K and G; 6. Preservation of Positivity from L)"K to K
  • 7. Signature Theorem for K Badly DisconnectedVII. TRANSLATION FUNCTORS; 1. Motivation and Examples; 2. Generalized Infinitesimal Character; 3. Chevalley's Structure Theorem for Z(g); 4. Z(l) Finiteness of u Homology and Cohomology; 5. Invariants in the Symmetric Algebra; 6 . Kostant's Theory of Harmonics; 7. Dixmier-Duflo Theorem; 8 . Translation Functors; 9. Integral Dominance; 10. Overview of Preservation of Irreducibility; 11. Details of Irreducibility; 12. Nonvanishing of Certain Translation Functors; 13. Application to (g, K) Modules with K Connected
Control code
ocn948756447
Dimensions
unknown
Extent
1 online resource (xvii, 948 pages)
File format
unknown
Form of item
online
Isbn
9781400883936
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
JSTOR
http://library.link/vocab/ext/overdrive/overdriveId
22573/ctt1bqrqp3
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)948756447

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